Algebra Examples

$- 3 x - 3 y \geq - 18$ $- x \leq - y$

Step 1

Solve $- 3 x - 3 y \geq - 18$ for $y$ .

Tap for more steps...

Step 1.1

Add $3 x$ to both sides of the inequality.

$- 3 y \geq - 18 + 3 x$

Step 1.2

Divide each term in $- 3 y \geq - 18 + 3 x$ by $- 3$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 3 y \geq - 18 + 3 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Divide $- 18$ by $- 3$ .

$y \leq 6 + \frac{3 x}{- 3}$

Step 1.2.3.1.2

Cancel the common factor of $3$ and $- 3$ .

Tap for more steps...

Step 1.2.3.1.2.1

Factor $3$ out of $3 x$ .

$y \leq 6 + \frac{3 (x)}{- 3}$

Step 1.2.3.1.2.2

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y \leq 6 - 1 \cdot x$

Step 1.2.3.1.3

Rewrite $- 1 \cdot x$ as $- x$ .

$y \leq 6 - x$

Step 2

Solve $- x \leq - y$ for $y$ .

Tap for more steps...

Step 2.1

Rewrite so $y$ is on the left side of the inequality.

$- y \geq - x$

Step 2.2

Divide each term in $- y \geq - x$ by $- 1$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- y \geq - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \leq \frac{- x}{- 1}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} \leq \frac{- x}{- 1}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y \leq \frac{- x}{- 1}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Dividing two negative values results in a positive value.

$y \leq \frac{x}{1}$

Step 2.2.3.2

Divide $x$ by $1$ .

$y \leq x$

Step 3

Find the intersection of $y \leq 6 - x$ and $y \leq x$ .

$y \leq N o (Min i m u m)$

Step 4